Having apparently got a capacitance measurement working, I thought I'd dismantle one of the cheap DHT11 sensors I bought.
Cutting the plastic cage off, reveals a tiny PCB with what looks like 5 surface mount resistors (but may be other components) and a 14 pin, unmarked chip on one side and the capacitance sensor on the other side.
I un-soldered the sensor, re-soldered it to a couple of wires and pins and plugged it into the Arduino board thus ...

"Herrrrrring" on the sensor gives the following readings ...

Quite a large range, 24pF to 2µF to play with. Not sure what happened with the readings in the middle, but it's been very stable sitting on the bench for the last ½ hour.